I actually don't completely subscribe to the theory that you can't live without a SIN and plenty of the information in Shadowrun describes that many many people live without them.. i.e. - the Sinless
I can't talk for Missions, but life without any SIN at all will generally become quite... tricky. You also can't get licenses for your restricted gear if you don't have a [fake] SIN.
You only need a license if the cops stop you and check you for one. Most runners try not to get stopped by, or even run into, police.
SR5 p. 367 System Identification Number (SIN)
No aspect of modern or legal life can function without a SIN. Those who don’t have one can’t get a job, can’t buy food, can’t even walk down the street.
This is also not actually true, since you can buy plenty of normal stuff with a certified credstick (i.e. - cash). Street vendors don't check your SIN if you have money. Once again if you live in a low lifestyle neighborhood many/most people don't have them so why would people be checking for them? They wouldn't and they couldn't or the SINless couldn't exist.
SR5 p. 84 Sinner (Layered)
A legal SIN is required for all legal purchases. This makes them very useful things to have, so those who are SINless generally get by with the use of fake SINs (p. 367) just so they can participate in society.
I guess they can try to live completely off the grid. Like homeless people or in a hut in the wilderness or something...?
They live at Low or Street level like other SINless people do.
A couple of things to keep in mind here Overbyte:
There is living a "sinless life" and then there is having a healthy life. In Shadowrun, these are exclusive.
A SIN serves as the primary form of identification in the SR universe. It is your citizenship, social insurance number and through extension, your driver's license, your bank account, your proof of ownership, and in some cases, your right to life!
Something as simple as getting a soycafe can not be done without without a SIN. Why? Well to get to the restaurant, you have to either walk, or take public transit. To take public transit, you need a SIN. To walk to the restaurant, you are required by law to broadcast a SIN... Even if you could get to the restaurant, chances are, it would be an automated process, again requiring you to use a SIN... Even if the place took certified Credsticks, you can bet, somewhere along the change of events, you would need a SIN (such as to transfer ownership of the soycaf from the restaurant to you!). And how did you get that Certified Credstick? To get one, you have to transfer money from an account with a SIN - at a bank branch- to the stic... which can't be done without a SIN.
When you get right down to it, there is no part of human society that isn't impacted by not having a SIN, fake or no.
People who live a Street lifestyle die. It's just a matter of when. Be it from the elements and exposure due to the fact the only shelter they can find is a cardboard box, a condemned building, or other makeshift enclosure. Their food is whatever has been thrown out, or whatever they can catch and kill, or whatever the soup kitchen is giving out -if they can stand in line long enough. There is no security for these people, as the very laws are written to exclude them! (A Citizen is entitled to the full protections of his/her/it country. But to be a Citizen, you have to have a SIN, as your SIN shows your Citizenship!). So the legal system sees them as non entities, as do the unfunded, and overwhelmed social services networks of countries. (Corps however, don't seem to have this problem. Oh right, trespassing laws...)
At least, that is the way it is for "law abiding" folks. Runners can and sometimes do fall outside this realm. For better or worse.